Open Window's Run dialog and enter the command: steam://open/console
The Steam Console will be launched. In the console, enter the following command: download_depot 312520 312521 [manifest ID]
Where [manifest ID] should be replaced with the version of Rain World that you want to download:
The specified version will begin to download. There is no progress bar, you just need to leave it running for a long while to let it complete. When it does successfully finish, it will tell you the location where it installed the old version. Typically this should be in: "Program Files/Steam/steamapps/content/app_312520/depot_312521"
If the downloaded version doesn't have a "UserData" folder in that folder, you'll have to create one, otherwise the game will freeze before you can get to the title screen.